New glueball-meson mass relations

Abstract

Using the ``glueball dominance'' picture of the mixing between $q\overline{q}$ mesons of different hidden flavors, we establish new glueball-meson mass relations which serve as a basis for glueball spectral systematics. For the tensor glueball mass $2.3\ifmmode\pm\else\textpm\fi{}0.1\mathrm{GeV}$ used as an input parameter, these relations predict the following glueball masses: ${M(0}^{++})\ensuremath{\simeq}1.65\ifmmode\pm\else\textpm\fi{}0.05\mathrm{GeV},$ ${M(1}^{\ensuremath{-}\ensuremath{-}})\ensuremath{\simeq}3.2\ifmmode\pm\else\textpm\fi{}0.2\mathrm{GeV},$ ${M(2}^{\ensuremath{-}+})\ensuremath{\simeq}2.95\ifmmode\pm\else\textpm\fi{}0.15\mathrm{GeV},$ and ${M(3}^{\ensuremath{-}\ensuremath{-}})\ensuremath{\simeq}2.8\ifmmode\pm\else\textpm\fi{}0.15\mathrm{GeV}.$ We briefly discuss the failure of such relations for the pseudoscalar sector. Our results are consistent with (quasi)linear Regge trajectories for glueballs with a slope $\ensuremath{\simeq}0.3\ifmmode\pm\else\textpm\fi{}0.1{\mathrm{GeV}}^{\mathrm{\ensuremath{-}}2}.$